LCM of 105 and 113
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 105 and 113 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 11865 as output. Here you can check the answer for Find the LCM of 105 and 113.
What is LCM of 105 and 113
Given Numbers are 105, 113
We can find the LCM of 105, 113 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 105 and 113
Multiples of 105 =105,210,315,420,525,630,735,840,945,1050,1155,1260,1365,1470,1575,1680,1785,
Multiples of 113 =113,226,339,452,565,678,791,904,1017,1130,1243,1356,1469,1582,1695,1808,1921,
Now, get the least common multiple of 105, 113 which is 11865
So, the LCM of 105, 113 is 11865.
Least Common Multiple (LCM) of 105 and 113 with the help of Prime Factorisation
One method for determining the LCM of 105 and 113 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 105's prime factorization:
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7.
105 = 31×51×71
And this is 113's prime factorization:
| 113 | 113 |
| 1 |
Prime factors of 113 are 113.
113 = 1131
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3, 5,7,113
.31×51×71×1131 = 11865
This shows that the LCM of 105 and 113 is 11865.
How to Calculate the LCM of 105 and 113 Using Common Multiples
The first step in determining the Least Common Multiple of 105 and 113 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 105 and 113:
Lets look at the first ten multiples of these numbers, 105 and 113:
105,210,315,420,525,630,735,840,945,1785 are the first ten multiples of 105.
113,226,339,452,565,678,791,904,1017,1921 are the first ten multiples of 113.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 105 and 113, for example, are 1260, 1785, and 1808. 11865 is the least common multiple since it is the smallest.
105 and 113 have an LCM of 11865.
Least Common Multiple of 105 and 113 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 113, than apply into the LCM equation.
GCF(105,113) = 1
LCM(105,113) = ( 105 × 113) / 1
LCM(105,113) = 11865 / 1
LCM(105,113) = 11865
Related Least Common Multiples of 105
Related Least Common Multiples of 113
Frequently Asked Questions on LCM of 105 and 113
1. What is the LCM of 105 and 113?
The LCM of 105 and 113 is 11865.
2. How to find the lowest common multiple of 105 and 113?
To find the lowest common multiple of 105 and 113, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11865.
3. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
4. What are the Factors of 113?
Answer: Factors of 113 are 1, 113. There are 2 integers that are factors of 113. The greatest factor of 113 is 113.
5. How to Find the LCM of 105 and 113?Answer:
Least Common Multiple of 105 and 113 = 11865
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 113
113 = 113
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11865 = 3 x 5 x 7 x 113
Step 4: Therefore, the least common multiple of 105 and 113 is 11865.